Upload
jerome-dorsey
View
214
Download
1
Embed Size (px)
Citation preview
Test #3 ReviewTest will cover Modules 12, 13, 14, and 15
Remember that logs of numbers are still just numbers. Please don’t turn them into decimals unless instructed otherwise, it’s like leaving a square root as a square root – it’s just prettier!
Do not be afraid of e. It’s just a number too. It just happens to be a super cool number that we can do a lot with.
This rule will be your friend:
Need to know facts:
Remember:
Exponential Functions:
Log Functions:
Forms:
where a > 0 and a ≠ 1.
where a > 0 and a ≠ 1.
You don’t have a chance at doing graphing transformations correctly if you don’t start with the correct parent function. Remember the 4 basic exponential/logarithmic shapes:◦ If you forget, you can always plug in a couple of points to help
you remember which one is which (you can even do this to check that you’ve done a transformation correctly!)
Need to know facts (graphing):
𝑓 (𝑥 )=𝑎𝑥 ,0<𝑎<1 𝑓 (𝑥 )=𝑎𝑥 ,𝑎>1
𝑓 (𝑥 )=log𝑎 𝑥 ,0<𝑎<1 𝑓 (𝑥 )=log𝑎 𝑥 ,𝑎>1
Need to know facts (graphing): Also, remember the vertical and horizontal asymptotes
of the parent functions to make it easier to see the asymptotes in the transformed ones.
𝑓 (𝑥 )=𝑎𝑥 ,0<𝑎<1 𝑓 (𝑥 )=𝑎𝑥 ,𝑎>1
𝑓 (𝑥 )=log𝑎 𝑥 ,0<𝑎<1 𝑓 (𝑥 )=log𝑎 𝑥 ,𝑎>1
𝑓 (𝑥 )=𝑎𝑥 ,0<𝑎<1 𝑓 (𝑥 )=𝑎𝑥 ,𝑎>1
𝑓 (𝑥 )=log𝑎 𝑥 ,0<𝑎<1 𝑓 (𝑥 )=log𝑎 𝑥 ,𝑎>1
Domain: all realsRange: (0, infinity)
Domain: all realsRange: (0, infinity)
Domain: (0, infinity)Range: all reals
Domain: (0, infinity)Range: all reals
Graph Adjustments Vertical Adjustments◦ f(x) + c
Moves graph up c units◦ f(x) – c
Moves graph down c units◦ 2*f(x)
Stretches vertically by a factor of 2 (could be any number > 1)
◦ 0.5*f(x) Compresses vertically by a factor of 2
(any fraction between 0 and 1)◦ -f(x)
Reflection over the x axis
Graph Adjustments Horizontal Adjustments
(usually backwards from what you expect)◦ f(x + c)
Moves graph left c units◦ f(x – c)
Moves graph right c units◦ f(2*x)
Compresses horizontally by a factor of (1/2) (could be any number > 1)
◦ f(0.5*x) Stretches by a factor of 2
(any fraction between 0 and 1)◦ f(-x)
Reflection over the y axis
Log Properties: Identity:
Inverse (I): ◦
Inverse (II):
Exponent to Constant:
Product:
Quotient:
Also…remember that ◦!◦ does not exist! And neither does the log of any
negative number because these values are not in the domain of the log!
Log Properties